Advanced MathHardSolving for the time in an exponential growth model
Advanced Math practice question
The population of an insect colony t weeks after observation begins is modelled by n(t) = 50 · 3^(t/2). After how many weeks will the population be 1,350?
Answer: 6
50 · 3^(t/2) = 1,350 → 3^(t/2) = 27 = 3³ → t/2 = 3 → t = 6.
Common wrong answers
- If you answered 3
- 3 is t/2, the exponent, not t.
- If you answered 12
- 12 comes from t/2 = 3 solved as t = 3 × 4, or from doubling twice.
- If you answered 27
- 27 is the value of 3^(t/2), not t.
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